Some recent measurements (Johnson et al., 1981) of the velocity variation with pressure (up to 2.0 bars) for lunar soils are compared with results from the Hertzian-contact theory. Contrary to the original contention of Johnson et al. (1981), the data are shown to be consistent with the results of the Hertz theory when the effects of nonrecoverable compaction are taken into consideration. A simple analysis given which shows that the velocity of loosely packed soil (which has only a fraction, f, of the grain contacts of a well packed soil) will be smaller than that of the well packed soil by the factor f1/3(0<f<1). A reanalysis of some earlier experimental data by Talwani et al. (1973) for the velocity variation with pressure (up to 2.5 kbar) of a volcanic ash also shows that the modified Hertzian-contact theory can be used to fit those data. It is found that the velocity function v(P) = 2.94P0.232 gives a better fit (rms error: ¿65 m/s) to the experimental data than a best fit equation of the form proposed by Talwani et al. (1973): v(P) = 1.147(1+(P/0.711)1/2-(P/2.45) which has an rms error of 84 m/s for the same data. The curves fitted to the data of Johnson et al. (1981) would give a velocity variation for the shallow lunar crust equal to v(z) = 225 (¿25)z1/6 m/s for z in meters (down to 64 m depth). This compared quite well with the velocity variation for the first 10 m of the Moon as interpreted by Gangi and Yen (1979), v(z) = 220z1/6, using the data from the Apollo 14 and Apollo 16 Active Seismic Experiments (up to 32 m separation) on the Moon (Kovach et al., 1971, 1972). The results reinforce the proposal by Gold and Soter (1970) and Gangi (1971, 1972) that the velocity variation in the very shallow lunar crust (the top 10 to 20 m) is due to self compaction of the lunar soil.